Question

A ball is thrown vertically with some velocity . A constant air resistance acts. If the time of ascent is `t_(1)` and that of descent is `t_(2)` , then
A. `t_(1) lt t_(2)`
B. `t_(1) gt t_(2)`
C. `t_(1) = t_(2)`
D. None

Answer 1

Correct Answer - A
Upward journey `R` : air resistance
Retardation : `a_(1) = ( mg + R)/(m) = g + (R )/(m)`
Let `h`: height attained by the ball
`h = (1)/(2) a_(1) t_(1)^(2)` (i)
Acceleration : `a_(2) = (mg - R )/(m) = g - (R )/(m)`
`h = (1)/(2) a_(2) t_(2)^(2)` (ii)
Equating (i) and (ii) , we get
`a_(1) t_(1)^(2) = a_(2) t_(2)^(2)`
`(t_(2))/(t_(1)) = sqrt((a_(1))/(a_(2)))= sqrt(( g + (R)/(m))/(g - (R)/(m)))`
`t_(2) gt t_(1)`